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<!DOCTYPE html>
<html data-require="math word-problems">
<head>
<title>Arithmetic word problems</title>
<script src="../khan-exercise.js"></script>
</head>
<body>
<div class="exercise">
<div class="problems">
<div>
<div class="vars">
<var id="ITEMS_PER_GROUP">randRange( 3, 12 )</var>
<var id="ITEMS_LEFT">randRange( 1, ITEMS_PER_GROUP - 1 )</var>
<var data-ensure="getFactors( ITEMS_PER_GROUP * GROUPS + ITEMS_LEFT ).length > 2"
id="GROUPS">randRange( 2, 12 )</var>
<var id="ITEMS_IN_GROUPS">GROUPS * ITEMS_PER_GROUP</var>
<var id="TOTAL_ITEMS">ITEMS_IN_GROUPS + ITEMS_LEFT</var>
<var id="NEW_ITEMS_PER_GROUP">getNontrivialFactor( TOTAL_ITEMS )</var>
<var id="NEW_GROUPS">TOTAL_ITEMS / NEW_ITEMS_PER_GROUP</var>
</div>
<div class="question">
<var>person(1)</var> is putting <var>itemPlural(1)</var> into <var>groupPlural(1)</var>.
If <var>he(1)</var> puts <var>plural( ITEMS_PER_GROUP, item(1), itemPlural(1) )</var>
in each <var>group(1)</var> <var>he(1)</var> will <var>groupVerb(1)</var>
<var>plural( GROUPS, group(1), groupPlural(1) )</var> and have
<var>plural( ITEMS_LEFT, item(1), itemPlural(1) )</var> left over.
If <var>he(1)</var> instead puts
<var>plural( NEW_ITEMS_PER_GROUP, item(1), itemPlural(1) )</var> in each
<var>group(1)</var>, how many <var>groupPlural(1)</var> of
<var>itemPlural(1)</var> can <var>he(1)</var> <var>groupVerb(1)</var>?
</div>
<p class="solution"><var>NEW_GROUPS</var></p>
<div class="hints">
<p>
<var>plural( GROUPS, group(1), groupPlural(1) )</var> of
<var>plural( ITEMS_PER_GROUP, item(1), itemPlural(1) )</var> each results in
<code><var>GROUPS</var> \times <var>ITEMS_PER_GROUP</var> = <var>ITEMS_IN_GROUPS</var></code>
<var>itemPlural(1)</var>.
</p>
<p>
<var>plural( ITEMS_IN_GROUPS, item(1), itemPlural(1) )</var> plus
<var>ITEMS_LEFT</var> left over equals
<var>TOTAL_ITEMS</var> total <var>itemPlural(1)</var>.
</p>
<p>
<var>plural( TOTAL_ITEMS, item(1), itemPlural(1) )</var>
divided into groups of <var>NEW_ITEMS_PER_GROUP</var> is
<code><var>TOTAL_ITEMS</var> \div <var>NEW_ITEMS_PER_GROUP</var> = <var>NEW_GROUPS</var></code>
<var>groupPlural(1)</var>.
</p>
</div>
</div>
<div>
<div class="vars">
<var id="ITEM_1_COUNT">randRange( 4, 12 )</var>
<var id="ITEM_1_COST">randRange( 4, 12 )</var>
<var id="ITEM_2_COST">randRange( 4, 12 )</var>
<var id="TOTAL_SPENT_ON_1">ITEM_1_COUNT * ITEM_1_COST</var>
<var id="TOTAL_SPENT">TOTAL_SPENT_ON_1 + ITEM_2_COST</var>
</div>
<div class="question">
<var>person(1)</var> bought <var>plural( ITEM_1_COUNT, storeItem(1, 1), storeItemPlural(1, 1) )</var>,
all costing the same amount, from the <var>store(1)</var> store.
<var>He(1)</var> also bought a <var>storeItem(1, 2)</var> for <var>plural( ITEM_2_COST, "dollar" )</var>.
<var>He(1)</var> spent a total of <var>plural( TOTAL_SPENT, "dollar" )</var>.
How much did each <var>storeItem(1, 1)</var> cost?
</div>
<p class="solution"><var>ITEM_1_COST</var></p>
<div class="hints">
<p>
Of the <var>plural( TOTAL_SPENT, "dollar" )</var>, <var>he(1)</var> spent
<var>plural( ITEM_2_COST, "dollar" )</var> on a <var>storeItem(1, 2)</var>, so <var>he(1)</var> must have spent
a total of <code><var>TOTAL_SPENT</var> - <var>ITEM_2_COST</var> = <var>TOTAL_SPENT_ON_1</var></code>
dollars on <var>storeItemPlural(1, 1)</var>.
</p>
<p>
<var>He(1)</var> spent <var>plural( TOTAL_SPENT_ON_1, "dollar" )</var> on
<var>plural( ITEM_1_COUNT, storeItem(1, 1), storeItemPlural(1, 1) )</var>,
so <var>he(1)</var> must have spent
<code><var>TOTAL_SPENT_ON_1</var> \div <var>ITEM_1_COUNT</var> = <var>ITEM_1_COST</var></code>
dollars on each <var>storeItem(1, 1)</var>.
</p>
</div>
</div>
<div>
<div class="vars">
<var data-ensure="getFactors( TOTAL_ITEMS ).length > 4"
id="TOTAL_ITEMS">randRange( 10, 99 )</var>
<var id="ITEMS">getNontrivialFactor( TOTAL_ITEMS )</var>
<var id="GROUPS">TOTAL_ITEMS / ITEMS</var>
<var data-ensure="NEW_ITEMS !== ITEMS"
id="NEW_ITEMS">getNontrivialFactor( TOTAL_ITEMS )</var>
<var id="NEW_GROUPS">TOTAL_ITEMS / NEW_ITEMS</var>
</div>
<div class="question">
When <var>person(1)</var> places <var>plural( ITEMS, item(1), itemPlural(1) )</var> in each
<var>group(1)</var> <var>he(1)</var> ends up with <var>plural( GROUPS, group(1), groupPlural(1) )</var>.
If <var>he(1)</var> wants <var>plural( NEW_GROUPS, group(1), groupPlural(1) )</var>,
how many <var>itemPlural(1)</var> should <var>he(1)</var> put in each <var>group(1)</var>?
</div>
<p class="solution"><var>NEW_ITEMS</var></p>
<div class="hints">
<p>
<var>plural( ITEMS, item(1), itemPlural(1) )</var> <code>\times</code>
<var>plural( GROUPS, group(1), groupPlural(1) )</var> <code>=</code>
<var>plural( TOTAL_ITEMS, item(1), itemPlural(1) )</var>.
</p>
<p>
If we divide the <var>plural( TOTAL_ITEMS, item(1), itemPlural(1) )</var> into
<var>plural( NEW_GROUPS, group(1), groupPlural(1) )</var>, then we get
<code><var>TOTAL_ITEMS</var> \div <var>NEW_GROUPS</var> = <var>NEW_ITEMS</var></code>
<var>itemPlural(1)</var> per <var>group(1)</var>.
</p>
</div>
</div>
</div>
</div>
</body>
</html>
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